Single pass RF driver

ABSTRACT

The disclosed embodiments relate to ion delivery mechanisms, e.g., for fusion power. Particularly, some embodiments relate to systems and methods for delivering ions to a fuel source in such a manner to initiate fast ignition. The ions may be accumulated into “microbunches” and delivered to the fuel with considerable energy and velocity. The impact may compress the fuel while delivering sufficient energy to begin the fusion reaction.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/046,822, filed Oct. 4, 2013, which claims the priority benefit of andis a nonprovisional application of U.S. Provisional Patent ApplicationNo. 61/710,521, filed Oct. 5, 2012, the contents of each which areincorporated herein by reference in their entirety for all purposes.

FIELD

Various of the disclosed embodiments relate systems and methods iongrouping and composition such as may be used, e.g., for achievingignition in nuclear fusion.

BACKGROUND

Nuclear fusion power has the potential to produce safe and clean energyin great abundance. Nuclear fusion does not produce as many radioactiveparticles as nuclear fission, produces more power than fission, avertsmany international complications by not producing weapons-gradebyproducts prevalent in uranium-based fission systems, and is easier andless dangerous to control during failure as compared to a runawayfission reaction. Unfortunately, the technology developments required toinitiate an economically significant fusion reaction are greater thanfor fission systems and so the latter has achieved more rapiddevelopment.

Several approaches presently seek to achieve sustainable fusion(producing more energy than was input to the system) with varyingdegrees of developmental success. For example, the National IgnitionFacility at Lawrence Livermore National Laboratory has sought to employa driver laser to compress fusion fuel. Laser energy presents manychallenges, however, and progress has not been as rapid as expected. Incontrast, more “conservative” inertial approaches, such as the Heavy IonFusion methods of the 1970s, remain, in many respects, more practicaland effective. In some instances, inertial methods employ proventechnologies including conventional accelerator designs using technologywhich have been extant since at least 1976. However, these acceleratorsystems often emphasize features appropriate for research purposes andtheir tools must be retooled, or complemented, before they can beemployed for power generation. Fuel ignition demands that considerableenergy be delivered in a short period of time and the power levels usedat most linear accelerators for research are inadequate.

Accordingly, there exists a need for tools which can complement orsupplement existing technologies to achieve the theoretical limitsrequired for fusion ignition.

BRIEF DESCRIPTION OF THE DRAWINGS

One or more embodiments of the present disclosure are illustrated by wayof example and not limitation in the figures of the accompanyingdrawings, in which like references indicate similar elements.

FIG. 1 illustrates a fuel assembly as may be employed in someembodiments.

FIG. 2 illustrates a perspective view of a fuel assembly as may beemployed in some embodiments.

FIG. 3 illustrates a general layout of components in a heavy ion drivenfusion energy complex implementing a Single Pass RF Driver System(SPRFDS) as may be employed in certain embodiments.

FIG. 4 is an abstract depiction of a microbunch in relation to anelectromagnetic wave as may be produced in certain embodiments.

FIG. 5 depicts a plurality of microbunches before the snugger, in thesnugger, the snug stopper, and after the snug stopper as generated insome embodiments.

FIG. 6 depicts a plurality of microbunches as may be adjusted in someembodiments.

FIG. 7 depicts the condition of the longitudinal phase space ellipses ofthe microbunches in a slug as they are input to the slick and at one ofmany possible final states following a slick as contemplated in someembodiments.

FIG. 8 illustrates a slick operation upon successive slugs of differentisotopes as may occur in some embodiments.

FIG. 9 illustrates the formation of a slug comprising multiple groups ofisotopes at the slick as may occur in some embodiments.

FIG. 10 illustrates modulation of the differential acceleration waveformat the slick as a means to shape the power profile of the beam on thepellet as may be implemented in some embodiments.

FIG. 11 illustrates the motion of microbunches spacing within a slug inthe longitudinal phase space (coordinates of momentum and time) early inthe slick process and at the fusion fuel pellet as contemplated in someembodiments.

FIG. 12 depicts relative microbunch placement within a slug at varioustimes as occur in some embodiments.

FIG. 13 depicts the further use of modulating the Slick RF waveform toshape the temporal profile of a Slug's power to create a pre-pulse at apellet as may occur in some embodiments.

FIG. 14 is a table depicting parameters of a driver pulse comprisingGroups of Isotopic Slugs which are chosen to locate the Bragg Peaks atthe end of the different ranges of the different isotopes in a givenGroup in relative proximity to each other in the pellet material.

FIG. 15 depicts a plurality of microbunches prior to impact in someembodiments.

FIG. 16 is a plot of the axial profile of the beam energy depositionrate illustrating the increased energy deposition in the Bragg Peak atthe end of an ion's range in the pellet material as may occur in someembodiments.

FIG. 17 depicts merging of beams in parallel linear accelerators fromfour beams in parallel beamlines to one beam, by a successive merges ineach of the two planes of the transverse phase space as may occur insome embodiments.

FIG. 18 illustrates the relative locations of the elements along thesection of beamline that terminates at the fusion fuel pellet in someembodiments.

FIG. 19 depicts a dynamic, compound beamline element to adjust theoverall focal length of the transport and focusing system from theSlicker to the fusion fuel pellet on a microbunch-to-microbunch basis asimplemented in some embodiments.

Those skilled in the art will appreciate that the logic and processsteps illustrated in the various flow diagrams discussed below may bealtered in a variety of ways. For example, the order of the logic may berearranged, substeps may be performed in parallel, illustrated logic maybe omitted, other logic may be included, etc. One will recognize thatcertain steps may be consolidated into a single step and that actionsrepresented by a single step may be alternatively represented as acollection of substeps. The figures are designed to make the disclosedconcepts more comprehensible to a human reader. Those skilled in the artwill appreciate that actual data structures used to store thisinformation may differ from the figures and/or tables shown, in thatthey, for example, may be organized in a different manner; may containmore or less information than shown; etc.

DETAILED DESCRIPTION

The following description and drawings are illustrative and are not tobe construed as limiting. Numerous specific details are described toprovide a thorough understanding of the disclosure. However, in certaininstances, well-known or conventional details are not described in orderto avoid obscuring the description. References to one or an embodimentin the present disclosure can be, but not necessarily are, references tothe same embodiment; and, such references mean at least one of theembodiments.

Reference in this specification to “one embodiment” or “an embodiment”means that a particular feature, structure, or characteristic describedin connection with the embodiment is included in at least one embodimentof the disclosure. The appearances of the phrase “in one embodiment” invarious places in the specification are not necessarily all referring tothe same embodiment, nor are separate or alternative embodimentsmutually exclusive of other embodiments. Moreover, various features aredescribed which may be exhibited by some embodiments and not by others.Similarly, various requirements are described which may be requirementsfor some embodiments but not other embodiments.

The terms used in this specification generally have their ordinarymeanings in the art, within the context of the disclosure, and in thespecific context where each term is used. Certain terms that are used todescribe the disclosure are discussed below, or elsewhere in thespecification, to provide additional guidance to the practitionerregarding the description of the disclosure. For convenience, certainterms may be highlighted, for example using italics and/or quotationmarks. The use of highlighting has no influence on the scope and meaningof a term; the scope and meaning of a term is the same, in the samecontext, whether or not it is highlighted. It will be appreciated thatsame thing can be said in more than one way.

Consequently, alternative language and synonyms may be used for any oneor more of the terms discussed herein, nor is any special significanceto be placed upon whether or not a term is elaborated or discussedherein. Synonyms for certain terms are provided. A recital of one ormore synonyms does not exclude the use of other synonyms. The use ofexamples anywhere in this specification including examples of any termsdiscussed herein is illustrative only, and is not intended to furtherlimit the scope and meaning of the disclosure or of any exemplifiedterm. Likewise, the disclosure is not limited to various embodimentsgiven in this specification.

Without intent to limit the scope of the disclosure, examples ofinstruments, apparatus, methods and their related results according tothe embodiments of the present disclosure are given below. Note thattitles or subtitles may be used in the examples for convenience of areader, which in no way should limit the scope of the disclosure. Unlessotherwise defined, all technical and scientific terms used herein havethe same meaning as commonly understood by one of ordinary skill in theart to which this disclosure pertains. In the case of conflict, thepresent document, including definitions will control.

System Overview

Various embodiments relate to ion delivery mechanisms, e.g., for use infusion energy systems. Particularly, some embodiments disclose a SinglePass RF Driver (SPRFD) from the vantage point of the final beamcompression and the potential advantages for ignition and high gainintroduced by components that shape the driver energy deposition inspace and time.

In some embodiments, the SPRFD provides methods for compacting the beamfrom the linear accelerator without storage rings. For example, theSPRFD may structure the ion delivery based upon the varied compositionof the isotopes. Magnetic switches on a first set of delay lines mayrearrange the internal structure of the various isotopic beams in someembodiments. A second set of delay lines may set the relative timing ofthe isotopic beam sections so they will telescope at the pellet, in oneof multiple fusion chambers.

Some embodiments contemplate a coordinated operation of the processesfrom the slick to the pellet, as described in greater detail below, soas to maximize the efficiency with which energy is delivered. Someembodiments consider the specific choices of isotope masses and in turntheir speeds according to the telescoping condition of equal magneticrigidity. The length of the slugs of different isotopes at input totheir particular slicks is another factor considered for beam linearrangement.

Maintaining the microbunch structure in some of the disclosedembodiments allows radiofrequency (RF) timing to synchronize operationsfrom pellet injection to ion source pulsing. The precision can beillustrated by, e.g., RF phase control of r1E-3 at 800 MHz, i.e., 1.25ps. The flexibility of this control accommodates different beam linelengths to multiple fusion chambers. This may provide SPRFD adaptabilityto geography, geology, and the built environment, which may facilitatevarious economies of scale.

Though various operations are discussed separately below, one willrecognize that they may be integrated in some embodiments. For example,the operations of the snugger and slick may be combined. In someembodiments, the slick may be a snugger without a snug stop. Thus, ionbunches in the snugger may come arbitrarily close to one another in someembodiments.

Fuel Assembly Overview

FIG. 1 illustrates a fuel assembly 100 as may be employed in someembodiments. Nuclear fusion occurs when two or more atomic nucleicollide at high speeds to form a new type of atomic nucleus (e.g, thecollision of two hydrogen nuclei to form helium). In some embodiments, acylindrical pellet may be used at the fuel cell. Nuclear fusionresulting from the collision process releases energy which may beharvested, e.g., using steam turbines or other known methods. Theconditions necessary to produce nuclear fusion can be difficult toproduce. Intense energy and pressure is necessary before the fuelmaterial will begin to collide so as to initiate fusion. However, theapplication of great energy to perform this compression may itselfimpart thermal motion to the fuel's atoms, thereby driving them fartherapart. To counteract the expansion effect, the fuel is often placed inan extremely cold environment and the compression energy is impartedextremely quickly and with considerable magnitude so as to compress thefuel before thermal expansion occurs. Fuel can be provided in discretepellets that are positioned one-by-one to receive the energy forcompression and ignition. Some or all of the fusion fuel may be in thesolid state when delivery of the compression and ignition energy begins.In some situations, the most practical fusion fuels are isotopes ofhydrogen and cryogenic temperatures are needed to solidify the fuel. Inthese situations, the fuel must be enclosed in an extremely coldenvironment (e.g., to prevent premature vaporization, expansion, andruination of the designed pellet geometry).

To accomplish these conditions, some embodiments contemplate an assembly100 that places the fuel 115 at the center of a cooled, cylindricalcasing of layers of high density material (e.g., lead) 140 which isbombarded by beams of high energy heavy ions, such as long range ions110 and short range ions 120 (though a cylinder is depicted here, othershapes, such as a sphere, may be used in some embodiments). The highenergy long range ions 110 and short range ions 120 can be delivered inequal beams to each end with extremely high power and energy to createhigh pressure in the casing materials to drive the fuel 115 inward. Theshort-range ions 120 may impact caps 145 a-b, to drive aquasi-hemispherical compression of the fuel material 115 in the endregions. Long-range ions 110 may penetrate an absorber layer 130 tocreate high pressure that expands and moves a pusher layer 135 tocompress the fuel, while outward expansion of the absorber layer can beresisted by the inertia of a tamper layer 125. The entire assembly maybe on the order of 1-3 centimeters in length and 1 centimeter in radius.This example depicts a “holhraum” pellet, though other pellets may beused in other embodiments as recognized in the art. For example, mayembodiments instead use a “spherical” pellet (sphinctering andcompression may occur in a spherical pellet just as in a cylindricalpellet).

Ions are arranged in some embodiments to impact the layers such thatBragg peaks 150 result “sphinctering” the fuel at a waist region,facilitating ignition. Particularly, in some embodiments quasi-sphericalimplosions are achieved at the ends of the cylindrical fuel pellets byselecting isotopes so that the higher energy deposition density at theBragg peaks 150 will drive “waists” (e.g., the sphinctering of thecylinder inward towards the longitudinal axis) to complement thequasi-spherical implosion of the end caps, as in FIG. 1.

Heating symmetry may be provided by 1 GHz circulation of beams aroundthe annular absorber layer 130, with time varying radius of the “hollow”beam. In some embodiments, the hollow beam may resemble a flying helicalspring, shrinking radially along the surface of a cone. The relativemodesty of the 100 g/cc density of the fuel material of embodimentsemploying a cylindrical fuel source may be tempered by the higherconvergence of cylindrical symmetry compared to spherical compression toa given density.

For increased pellet gain fusion yield, and overall confidence ignition,various embodiments propose a means to sequester the fuel near the endcaps 145 a-b that is slated for fast ignition. For efficient use of thebeam energy, short-range ions 120 may be used to heat appropriatelyshaped, thin end caps 145 a-b with a distribution of heat energy thatcan drive a quasi-hemispherical compression at these ends in someembodiments. Various embodiments extend this to quasi-sphericalcompression in the fast ignition zones by driving waists in the cylinderat locations about twice the initial fuel radius in board from the endcaps 145 a-b. In some embodiments, the rapid rising temperature afterfast ignition will intensify the propagating burn and promotepropagation through the waists toward the large mass of fuel in thecenter section.

FIG. 2 illustrates a perspective view of another exemplary fuel assembly215 as may be used in some embodiments. Here a spherical fuel capsule230, rather than a cylinder is used, though ions entering at each end ofthe assembly 215 are again used to compress the fuel material. Theassembly 215 may be immersed within a lithium chilled “sabot” 210 whichmay itself be contained within a lithium volume 205 at room temperature.

Achieving the desired characteristics of the ion beams is very importantto initiating fusion (e.g., the density and temporal profile of powerand energy deposited in specific regions of the pellet casing). The ionsmay be accelerated by a linear accelerator and subsequently compacted inspace and time by beam handling processes generically called“manipulations” prior to impacting the fuel so as to achieve the desiredtemporal and spatial heating characteristics.

Braggs Peak Considerations

Some embodiments contemplate means to sequester the fuel at the fuelends slated for fast ignition. Driving the end caps with short-rangeions can allow compression to be quasi-hemispherical. Some embodimentsextend this to quasi-spherical in the fast ignition zones, by drivingwaists in the cylinder at locations about twice the initial fuel radiusinboard from the ends.

The use of Bragg peaks to promote quasi-spherical compression in thefast ignition zone presents a method where large advantages may accruethrough exploitation of multiple isotopes. Such potential advantages caninclude reducing convergence in the fast ignition zone, from ˜18 forcylindrical to ≤10 for quasi-spherical compression, and reducing thenecessary density of the bulk of the fuel to that which will supportburn propagation from robustly burning ends.

Regarding the use of Bragg peaks to drive waists (e.g., to drive thefuel inward), FIG. 14 depicts placement of the Bragg peaks of groups andisotopes within groups. Different isotopes may be used to adjust theshown placements. The Bragg peaks of different isotopic slugs may belocated at different axial locations in the pellet, e.g., at the end ofthe different ranges of the different isotopes due to their differentenergies.

The isotopes can be chosen so that the ranges serve different purposesin driving the pellet, e.g.: 1. Compress the barrel of the pellet: range˜equal to the length of the barrel; 2. Drive the end caps in ahemispherical compression: range<thickness of end caps; 3. Drive the“wasp-like” waists to sequester fuel for the end regions, where fastignition will occur, and drive the other half of the compression of thatfast ignition fuel in a quasi-hemispherical fashion, which may work withthe quasi-hemispherical compression of the end caps to achieve aquasi-spherical compression, which may help to avoid excessiveconvergence (which may lead to failure of NIF to ignite); 4. Heat thenecessary (relatively small, e,g, if pre-compressed) amount of fuelneeded to ignite a propagating burn but every isotope may pile into thefuel mass, even though some isotopes may spread their energy over morethan just the “blasting cap” mass.

Plant Topology

FIG. 3 illustrates a general layout 300 of components in a power plantimplementing a SPRFD system as may appear in certain embodiments. Thedifferent ion species can be emitted from separate ion source intoparallel beamlines, accelerated by high voltage DC in the parallelbeamlines, and converted (by “RF capture”) into strings of discretemicrobunches in the first RF accelerator section, where the microbunchesmay move at the speed of the nominal ion. As the same-species grouptogether, they form “microbunches”. Microbunches may be transmittedtogether in successive iterations, known as “slugs”. For example, fourslugs may be transmitted, each slug containing 10 microbunches of 10different ion species (thus, 40 microbunches are transmitted in total).The slugs may themselves be grouped prior to impacting the fuel, or maybe arranged to impact successively.

After RF acceleration gives the ions a substantial speed to facilitatecontrol by magnetic fields, the beams of microbunches may be alignedinto a common beamline at stage 305 before being accelerated through themain linear accelerator 310. Alignment may use pulsed bending magnetsoperating in spaces between beam sections of different isotopes, saidspaces having resulted from the timing of emission from the differention sources for the different isotopic beams. The structure of eachisotopic beam section may also contain time gaps that will later be usedto manipulate sub-sections of each isotopic beam, e.g., slugs. The timegaps that separate the slugs (e.g., eight per isotope) may be created bythe action on the ions of features provided in the electric and magneticfields from (and including) the ion source up to the aligner stage 305.

Ions of different species may be accelerated at different speeds. As thesame-species group together, they form “microbunches”. In someembodiments, ions of different species are accelerated to the same speedat every station along the main accelerator by appropriate adjustment ofthe amplitude of the accelerating RF fields. The time interval needed toadjust the RF field amplitude can be provided by causing a beam to beemitted from the different isotope source in a specific time series.This can result in the beam sections of the different isotopes beingstaggered in the parallel beams up to the aligner.

Microbunches may be transmitted together in successive iterations, knownas “slugs”. For example, four slugs may be transmitted, each slugcontaining 10 microbunches of 10 different ion species (thus, 40microbunches are transmitted in total). The slugs may themselves begrouped prior to impacting the fuel, or may be arranged to impactsuccessively.

Following acceleration, a snugger 315 may move the microbunches closertogether within the slug. The snugger may bring the microbunches closerto a single position in each slug (e.g., the slug's center of mass). A“snugstop” may also be used to lock microbunch spacing for transportacross various distances to multiple chambers. In some embodiments, thesnug-stop removes the ordered, differential, microbunch-to-microbunchenergy/momentum/speed differences. In some embodiments, snugging andslicking comprise a single operation and there is no longer a snugstopper.

The slugs may then travel through a telescoper 320, slug delay line 325,and isotope delay line 330, to bring the slugs in closer proximity withone another. In some embodiments, the plant includes many fuelassemblies in different focuses 345 a-f. The slugs may be passed tothese assemblies after travelling through a slick 335 a-d and wobbler340 a-c. The telescope may be used to accelerate the different isotopicspecies to the different speeds that will give all isotopic species thesame magnetic rigidity. The function of the merge is to reduce thenumber of parallel beams in anticipation of the reconfiguration tofollow in the slug delay line. The merge may increase the transversephase space in order to maintain the longitudinal phase space withinbudget. The slug delay line 325 may be used to progressively switchsuccessive slugs of each isotope so that the single beam comprisingmultiple slugs (e.g., eight) from the merge is converted into multipleparallel beams in separate beamlines (e.g., sets (e.g., two) of fourslugs).

The isotope delay line 330 may remove time gaps, which were enlarged bythe foregoing manipulations, between slugs of different isotopicspecies. The time gaps between isotopic species after the isotope delayline may be such that the different speeds of the different isotopeswill result in the slugs of different isotopes arriving at the fuelpellet according to the schedule designed for pellet compression andignition. The variation in these time gaps to accommodate differentoverall length of beamline to the multiple chambers can be provided bytiming of the pulsed emission from the ion sources for the variousisotopes. The slugs may be passed to these assemblies after travellingthrough a slick 335 a-d and wobbler 340 a-c. The slick may be used tobring the microbunches of the slugs close together, overlap to variousbunches as desired, and shape the bunches in time to build the desiredpulse shape in three spatial dimensions and time. In some embodiments,the plant includes a number of fusion power chambers 345 a-f, in whichthe operations may be identical or may be different with correspondinglydifferent beam parameters established by corresponding pulse-to-pulseoperation of the various ion sources and beam manipulations

Overview of Components for Microbunch Manipulation—Telescoping,Snugging, Slicking, etc.

Telescoping can be a very powerful feature for getting ions into theassigned small volume and mass of the target in the short time demanded.Telescoping may adjust the accelerating gradients in the linearaccelerator so that all isotopes have the same given speed as they passa given spot in the linear accelerator. This can allow one linearaccelerator to accelerate all the different isotopes. The last stage ofthe linear accelerator can have successive “off ramps” where eachisotope is diverted into a “common magnetic rigidity” beamline (e.g.,telescoping beams).

The timing of the different isotopes can be such that they all arrive atthe pellet at the same time, ±a fraction of a nanosecond. Thetelescoping system can be synchronized by the RF fields over the whole20+km construct.

At a high level, a slick is a snug without a snug stop. Differentiallyaccelerated microbunches may keep getting closer and may even startoverlapping. Each microbunch elongates as a result in part because ofthe spread of momentums in each microbunch. The second elongating effectof the microbunches can be due to the space charge forces: ions at thefront tip of a microbunch are sped forward, etc.

Snugging and slicking can include differential acceleration frommicrobunch to microbunch within a slug. A slug may alternatively bereferred to as “a macropulse of micropulses of a given isotope.” Thegeneral difference between a snug and slick operation, as discussed invarious places herein, is that when a snug is used independently of aslick, the snug is intended to be “partial”, e.g., the microbunches donot overlap and interpenetrate—they just become closer together. In thatcase, there will be km more of beamline before the pellet. In such acase, the several percent differences in energy/momentum/speed can beremoved at the end of the snug to “freeze” the microbunches in theirrelative positions, which can be closer together after the snug thanbefore being snugged. The “stand alone” snug (e.g., Snug alone=Snug+SnugStop) may require a substantial length of accelerator to remove theenergy differences input to produce the snugging effect.

Another reason for delaying the Snug and incorporating it into the Slickcan be the higher space charge forces that result when the microbunchesare squished into smaller groupings in three dimensions (in the movingframe of reference).

This latter consideration can be accommodated in some embodiments byintegrating a snug with a slick, and the microbunches are longer (morespread out in space) with lower space charge fields until the slick. Afurther effect may be to allow the stretching of microbunches as abovecan reduce the space charge forces. This effect can be counter-intuitivewhen the intent is to compact the beam.

In some embodiments, the net effect of the set of operations becomesgreater than the sum of the parts. The drop in peak current of themicrobunches can be overcome when they slick into a pileup (in threedimensional space and time) while “sliding over each other” in thelongitudinal phase space (e.g., the distribution of the relativemomentums of the ions vs. their relationship in time).

The parameters for slick can be derived by requiring that themicrobunches not be longer than needed to play their part in buildingthe overall driver pulse power deposition in the pellet in space andtime. For instance, in some situations the start of the Slick cannot betoo far from the pellet, or the individual microbunches will stretch toofar and lose the peak power they need to have at the pellet.

Differential acceleration of microbunches can be effected by offsettingthe frequency of the slick or snug RF cavities. By decelerating thefirst microbunches more than successive microbunches less (e.g., by moreor less linear progression of Slick/Snug “kicks”) the RF wave completesless than a full cycle from the time that one microbunch passes throughto the time that the next microbunch passes through. The term “bunchfrequency” may be used herein to refer to the rate of passage of bunchesvs. the RF frequency of the accelerator structure. Within a Snug/Slick,the bunch frequency can be higher than the RF frequency. If there areSnug Stop accelerator section in an embodiment, its frequency can beless than the bunch frequency.

Microbunch Structure

FIG. 4 is an abstract depiction 400 of the longitudinal phase space ofvarious microbunches 410 a-c in relation to an electromagnetic wave 405(e.g., an RF wave) as may be produced in certain embodiments. Here thehorizontal axis depicts time. A microbunch may be a collection of ionsin the same isotope species, e.g., as discussed above. In someembodiments, amplitude modulation of the wave is a means to shape thepower of each slug upon impact. The sum of the shapes of individualisotopes in the three spatial dimensions and time may be used to build adetailed driver profile. Together a string of microbunches 410 a-c maycomprise a “slug” and a section of the beam of an individual isotope maycomprise a series of “slugs. Upon the same waveform 405 may reside anearly microbunch 410 a, a middle bunch 410 b, and a late bunch 410 c.Each ion species may possess a different weight (e.g., different neutroncount) and may be accordingly accelerated at a different rate.

To allow precise control of timing, the beam structure of discretemicrobunches may be maintained by applying suitable RF fields during thebeam manipulations that follow the principal RF acceleration, whichinputs the beam energy. The frequency of microbunch-maintaining RF fielddetermines the length of the microbunches, which can have significancefor the number of ions that may be transported in each microbunch. Inone example, microbunches are transported at 800 MHz. With eachmicrobunch comprising an efficacious number of ions (where the totalbeam for an effective compression and ignition pulse may comprise, e.g.,160,000 microbunches at the first RF accelerators of all beamlines,becoming 40,000 microbunches after a four-fold, e.g., merge), the spacecharge field at the tips of the microbunches will be of the order of 1MV/m, which may be a fraction of the RF field gradient (10 MV/m)attainable in RF cavities operating at 800 MHz, and therefore may betransportable without deleterious effects on the beam quality (phasespace). Beam neutralization may be needed after the differentialacceleration until adjacent bunches begin to overlap.

In one example, microbunches are transported at 800 MHz, which resultsin the space charge field at the tips of the microbunches being 1 MV/m,which may be a fraction of the RF field gradient (10 MV/m), through beamcompaction processes upstream from the differential accelerator.

In some embodiments, the merge shines four beams into the same space.This can increase the transverse emittance because of the requiredangular difference in the directions of the merging beams. Largeremittance may mean larger spot size on the pellet, which means lessintense heating, etc. Accordingly, some embodiments seek to reduceemittance.

In some embodiments, the permissible amount of microbunch lengthening isset by the design pulse shape at the pellet, which may vary fordifferent groups of isotopes. As one possible example, the variousisotopes can be selected in groups that have narrow bands of ranges(stopping distances in the target). For the overall set of isotopes ofthe various groups, the ranges may extend from 1 to 10 g/cm². The rangesof the isotopes within the various groups can be selected to drive thecylinder barrel (longest ranges) and thin hemispherical endcaps (shortranges), to heat the 0.5 g/cm² ρR fast ignition zone (where ρ is thefuel density and R is the radius) at the culmination of the compressionand ignition process.

In some embodiments, the ranges of designated groups of isotopes can beselected so that the end of their ranges fall at designed axialstations, within a distance of each other, part way toward the midplaneof the cylinder from each end. With such selection of ion ranges, theBragg peaks at the end of the ranges can increase the specific heatdeposition density, which in turn can create higher pressure than inadjacent material, which in turn will accelerate the implosion of thecylinder at these axial stations. In this manner, the acceleratedimplosion can drive an annular wedge or waist, forcing the affectedpusher and fuel material either toward the cylinder midplane or towardthe cylinder ends. Driving such waists at appropriate axial stations maywork in conjunction with the hemispherical implosion of the endcaps toachieve quasi-sphericity of the compression of the fast ignition zonesat the pellet's ends. To the extent the resulting implosion of the endzones approaches spherical, the convergence factor (ratio radii of fuelbefore and after compression) can be reduced from that required forsimple cylindrical compression. A low convergence factor may bedesirable as it is a primary metric for susceptibility to hydrodynamicinstability of the implosion.

Such lengths may improve the quasi-sphericity of the compression of thefast ignition zones at the pellet's ends. In some embodiments, momentumdifferences between microbunches are input in a correlated andtime-ramped fashion to contribute to beam compaction. Beam linetransport elements with time-ramps located close after the differentialaccelerator geared to the ramped momentum differences may be used tocompensate the normal effect of ions with different momenta to focuswith different focal lengths the associated shifts of focal point. Toaccomplish this compensation on the desirable microbunch-to-microbunchbasis, the compensating fields may be applied before the microbunchesoverlap substantially. Thus, the dynamic beam line elements may belocated suitably close after the differential acceleration.

In some embodiments, momentum differences between microbunches arecorrelated and time-ramped. Beam line transport elements located closeafter the differential accelerator may be used to correct the associatedshifts of focal point. Beam neutralization may be needed after thedifferential acceleration until adjacent bunches begin to overlap.

In some embodiments, concurrent collapse of each isotope and telescopingof the isotopes may cause the current in each beam line to rise rapidlyduring the final microsecond of driver pulse generation.

Microbunch Snugger Interaction

FIG. 5 depicts a plurality of microbunches before the snugger, in thesnugger, the snug stopper, and after the snug stopper as generated insome embodiments.

The snugger and the slicker may both be RF accelerator “structures”(cavities/resonators/etc.) whose resonant frequency may differ (e.g.,about 0.1% or so in some embodiments) from the frequency with whichmicrobunches arrive and pass through. The effect can be for successivemicrobunches to fall on different phases of the RF wave, either moredeceleration/acceleration or less: decelerated microbunches fall backtoward the center microbunch, and trailing accelerated microbunches movetoward the center microbunch.

In some embodiments, the temporal structure of the slugs is establishedin the snug process, which moves microbunches closer together thanemitted from the main linear accelerator, squeezing each microbunch inlongitudinal phase space. In some embodiments, the compressedmicrobunches became the completed slugs when four parallel beams fromthe linear accelerator are merged, two by two, in transverse phase space(e.g. as depicted in FIG. 17). This slug structure may be preserved,along with the phase space of the individual microbunches, by thecontinuation of phase focusing, through delay lines and beam transportup to the slick.

In some embodiments, the finest timing for the schedule of arrival ofdifferent isotopic slugs at the pellet may be obtained by RFsynchronization. Microbunch timing may be controlled in the beamlinesbetween the linear accelerator and slick by RF sections that alsomaintain the longitudinal phase space by inverting the longitudinalphase space ellipses at intervals along the beam path. The microbunchslug structure within a slug may be preserved, along with thelongitudinal phase space of the individual microbunches, by the placingRF cavities at specified intervals along the beam path, through delaylines and beam transport up to the slick.

In some embodiments, this microbunch maintenance can be provided bycavities having RF frequency equal to the frequency of arrival of themicrobunches and maximum applied RF voltage equal to twice thedifference of the maximum (or minimum) momentum from the nominal. Thecavities can be placed so as to act on each microbunch when the momentumspread of the ions in a microbunch has caused its longitudinal phasespace ellipse to shear to a specified maximum length and time duration.This may be set by the period of the RF cavities and the maximum phaseangle of the RF wave. These cavities may accommodate the naturalshearing by inverting the longitudinal phase ellipses for eachmicrobunch. The phase space ellipse may then resume shearing, startingfrom a “backward” tilt and proceeding until the tilt is again themaximum in the “forward” sense, where it will again be inverted by thenext set of RF cavities.

In some embodiments, the timing of the end product slugs may be toocoarse relative to the precision of the pulse timing and power profileneeded at the fusion pellet. For example, the precision ultimatelyavailable is determined the accuracy of RF phase control (e.g., ±1E-3)of the RF period at the highest frequency used (e.g. 800 MHz), whichwould be ±0.00125 nsec. This precision may depend, however, on thetiming of the reference microbunch, which is identified at the frequencyof RF capture in the first RF accelerator section, where the precisionwould be ±one-half of that RF period. For example, at 12.5 MHz theinitial timing precision of the reference microbunch will be within thebounds of ±4 nsec. This would be more than ten times coarser than neededfor some aspects of the pellet implosion, especially in regard to fastignition. Using non-intrusive beam observation methods to track thereference microbunch through the series of frequency doublings in thelinear accelerator, it is possible to determine the divergence of thetiming of the reference microbunch from its specified timing. To bringthe timing of the reference microbunch (and thereby the entire slug)much closer to that ultimately possible, for example ±0.00125 nsec aspossible at 800 MHz, tbaseline of the snug's offset-frequency RF may beadjusted according to the need of each individual isotope as depicted inthe dashed lines 605 on FIG. 6. As a result, in some embodiments theslug will move either closer to or farther from its neighbors at thesame time that its microbunches move closer together.

In some embodiments, snugging reduces the time gap between successivemicrobunches by differential acceleration whereby the first microbunchof a Slug is decelerated the most, the last microbunch is acceleratedmost, and the first half of the microbunches are deceleratedprogressively less and those in the second half are acceleratedprogressively more. The differential acceleration is accomplished by RFaccelerator cavities whose resonant frequency differs by a precise,small amount from the frequency of arrival of the discrete microbunches.Frequencies of the RF cavity less than the microbunch arrival frequencymay result in the RF field completing less than a full cycle betweenmicrobunches, causing successive microbunches to “walk up” the RF wave.

To enable transport of the beam after the snug with microbunch structureintact and acceptable momentum differences, the differences between thespeeds and momenta of successive microbunches may be removed when thedesired degree of snugging has been achieved. This snug stop can beaccomplished by RF cavity frequencies larger than the microbunch arrivalfrequency, causing successive microbunches to “walk down” the RF wave,from maximum acceleration of the first microbunch to maximumdeceleration of the last. The total of the differential acceleration foreach microbunch can be exactly opposite to that of the Snug, but SnugStop operates on microbunches that arrive at the higher frequencyresulting from having been Snugged closer together in time.

FIG. 6 depicts an example plurality of microbunches to represent a slugas they receive the differential acceleration to drive the snug process(left side of figure) and as they receive the equal and oppositedifferential acceleration to stop the snug process (snug stop) when themicrobunches are closer together at the end of the snug process as usedin some embodiments. The figure also shows (dotted lines 605) theraising or lowering of the baseline of the differential accelerationthat may be used to move the slug as a whole forward or backwardrelative to its neighbors to correct the relative timing between slugsand achieve the high precision possible with RF phase control at thehigher frequencies of the RF field and microbunch arrival.

Following the slick linear accelerator section and until reaching thepellet, the momentum spread within each microbunch may cause themicrobunch to stretch in time. Space charge may tend to increase theelongation, but the initial effect on every microbunch may wash out(except for the ones on the extreme ends of slugs) when consecutivemicrobunches overlap. This may occur rapidly because of the bunches'close spacing at 2 GHz.

Microbunch Slick Interaction

In some embodiments, the slick is the last accelerator process to workon individual microbunches. In some embodiments, the slickdifferentially accelerates microbunches within each slug so that theleading microbunches slow down and the trailing microbunches speed up.

In some embodiments, to snug or slick, successive bunches receive lessand less deceleration until the zero crossing and then receiveincreasing acceleration. This can mean the RF cycle is longer than thetime between microbunches. A snug stop may reverse these features: thefirst bunch accelerated most and the last bunch decelerated most. Manyembodiments omit the use of a snug stop and in some embodiments,snugging and slicking operations are approximately the same.

The term “slick” is suggested by the motion of the microbunches for agiven isotope as they “slide over” one another in the longitudinal phasespace during the approach to the pellet (See, e.g., FIG. 11).

FIG. 7 depicts microbunch inputs to the slick as contemplated in someembodiments. For example, FIG. 7 depicts the condition of thelongitudinal phase space ellipses of the microbunches in a slug as inputto the slick and at one of many possible final states at the fusionpellet resulting from slick as contemplated in some embodiments. Theparticular final state shown is the case where all microbunches in aslug arrive simultaneously at the pellet. To provide desired temporalpulse profiles, the amplitude of the slick RF may be modulated in avariety of ways.

As discussed herein, some embodiments contemplate substituting storagerings with bunching operations. The organized slugs may then travel byinduction cavities with a ramped accelerating field. In the slick, thedifferentially accelerated microbunches may move with respect to oneanother in the longitudinal phase space, leaving behind the empty spacesoriginally between them. The longitudinal phase space per microbunch, asemitted by the linear accelerator may become an asymptotic potential forfocusing. The correlation of the momentum differences betweenmicrobunches can be used to compensate for differences.

Whether it is SPRFD's microbunches or compression of a single long pulseof beam, a ramped beamline transport component may have similar effects.The final compression by RF “tilting” (e.g., accelerates anddecelerates) of the string of microbunches can provide precision timingof RF synchronization. In some embodiments, the pulse shape at thepellet sets the permissible amount of microbunch lengthening in the beamline to the pellet. In some embodiments, the overall duration of theslug at the pellet must fit the part of the pulse that it serves, andthe microbunches must be no longer than their respective slugs.

Accordingly, the microbunch width may establish the maximum driftdistance for the slug and in turn the parameter sets for the initialmacropulse durations (thus energy content for each slug), range ofmomentum/speed/energy kicks, applied RF voltages for each isotope, andmany other factors. When the duration of the (former) microbunches issignificantly less than the necessary slug duration, modulation of thedifferential acceleration allows shaping each slug at the pellet, asillustrated in FIG. 10.

For example, each microbunch of the fastest isotope (20 GeVXe) havingmomentum spread 0.05% (for the SPRFD embodiment with 800 MHz microbunchmaintenance), can lengthen to 10 ns during a drift of 3 km. Being boththe fastest isotope and serving the longest features of the pulse shape,Xe will have the longest drift distance, and also will contribute themost energy per Slug.

In some embodiments, isotopes are selected for groups, 2-6 isotopes ineach group, having narrow bands of ranges suited to different roles indriving the pellet. These roles may include: 1. compressing the cylinderbarrel (or spherical chamber); 2. driving the end caps in ahemispherical compression; 3. driving the waists (e.g., the regionsalong the cylinder following the end caps); and 4. driving fastignition. The number of ion groups involved may be larger than thesefunctions, and ion groups may be assigned to different functions (or tothe same function). The narrow bands may have energies given by thetelescoping system of equal magnetic rigidity (e.g., 239T-m for20GeVXe-130). These ranges may, e.g., extend from 1 g/cm2 to 10 g/cm2.Xe-like isotopes at 20 GeV drive the 1 cmPb cylinder barrel, whereasPb-like isotopes at 13 GeV may drive 0.1 cm thick hemispherical Pb endcaps. The 1 g/cm2 ranges efficiently heat the fast ignition zone, whereρL 1 g/cm2 agrees with ρR 0.5 g/cm2.

To achieve quasi-sphericity of the fuel compression in the fast ignitionend zones, in conjunction with the use of short range ions to heat thethin end caps and drive hemispherical compression of the fuel containedtherein, Bragg peaks of intermediate range isotopes may drive waists inthe barrel near each end of the cylindrical fuel mass to sequester thefuel destined for fast ignition and promote sphericity of its implosion.Compared to cylindrical compression, spherical compression may have theadvantage of requiring a lower convergence factor (ratio of the initialto the final radius of the fuel mass) to achieve a given final fueldensity, where implosions with smaller convergence ratios are less proneto the hydrodynamic instabilities that spoil the compression process. ABragg peak refers to the substantially increased rate of energydeposition exhibited by heavy ions near the end of the range, asillustrated, e.g., in FIG. 16. The resultant increased specific heatingof the absorber material can result in increased pressure in thevicinity of the Bragg peaks relative to the adjacent material, which canaccelerate the implosion at those locations and cause a sphincter-likemotion to pinch waists into the pellet.

The ability of the SPRFD to focus to smaller spots than previous HIFdriver designs provides a means to avoid the issue regarding the shiftof the location of Bragg peak as the absorber material expands,decreasing the material density, and lengthening the distance needed toreach the end the range, which is the product of density times pathlength. In some embodiments, rather than constantly heating virtuallythe entire annular absorber, the smaller spot may heat a narrow annulusat any instant. Therefore, whereas the density of a continuously heatedabsorber mass will drop as the heating causes it to expand, theseembodiments' smaller spot may be dynamically aimed, by programming themodulation of the wobbler fields to adjust the radius of the hollowbeam, at the inner edge of the annulus that has just been heated, tomaintain the track of the ions in material that has had less time toexpand so that the ions see a density that remains nearly constant. Forexample, whereas the radius of the spot of previous HIF drivers is ofthe order of 1 mm, SPRFD may focus to 0.1 mm radius or less. For theannular absorber, the mass of the heated annulus can be proportional itsthickness (e.g., twice radius of the beam spot), and in some situationsa beam of a given power will heat an annulus of a given thickness tentimes faster than it will heat an annulus that is ten times as thick.

FIG. 8 illustrates the formation of a slug comprising multiple groups ofmicrobunch isotopes at the slick as may occur in some embodiments.Particularly, FIG. 8 illustrates some basic considerations regardingdesign of the Slick operation to accommodate successive Slugs ofdifferent isotopes as may occur in some embodiments. In general, theconsiderations illustrated regard the time factors that set requirementson the maximum length of the slugs, the time between the trailing edgeof one slug and the leading edge of the next slug. RF technology may seta minimum time for resetting the phase (rephasing) of the RF cavities inthe time between the end of the passage one isotopic slug and thebeginning of the next slug. The length of a slug can be an importantdeterminant of the total amount of energy that a slug may carry anddeliver to the pellet. The total time between the reference points inthe different slugs time may set the distance that the differentisotopes may telescope, which, in conjunction with other factors, mayset the requirement for the difference in speed between the isotopes.These factors affect the distance from the slicker to the fusion pellet,the amount of differential acceleration that is needed to accomplish thedesired slick in the defined distance to the pellet, and otherassociated parameters. Internal consistency may require, for example,that the desired slick effects and the desired telescoping take placeover the same distance.

FIG. 9 illustrates some considerations regarding application of theslick operation to successive groups of isotopic slugs. The differentgroups in this example comprise isotopes using a common set of RF slickaccelerating cavities. In this manner isotopes in a group haverelatively small differences in speed for telescoping may be produced.Different groups of slugs may use different sets of RF slickaccelerating cavities to accommodate the need for the period of theresonant RF cavities to correspond to the period between microbunchestraveling at the substantially different speeds that characterizedifferent groups. These considerations may include those applicable toslick of different slugs by a single slicker, but also additionalconsiderations, e.g. that the RF fields in a slicker for one group ofslugs must be off during passage of the slugs belonging to anothergroup. These factors may determine the locations of the slickers for thevarious groups of isotopic slugs, and define requirements for internalconsistency between the lengths of all slugs, the various distances tothe fusion pellets, and others.

FIG. 10 illustrates modulation of the differential acceleration waveformat the slick as a means to shape the power profile of the beam on thepellet as may be implemented in some embodiments. In the example of FIG.10, modulating the waveform of the slick RF shapes a Slug's profile atthe pellet. In the top portion of the figure, application of equalamounts of differential acceleration from microbunch to microbunchresults in reducing the distance between successive microbunches by theequal amounts for all microbunches. The figure shows the case where allmicrobunches arrive simultaneously at the pellet. In a general case, themicrobunches may arrive at the pellet with their centers spaced by anyconstant distance. The bottom figure shows application of a RF waveformcomprising two linear portions. The result shown adjacent to the rightof that arrangement of waveform and microbunches shows the resultingconfiguration of the microbunches at the pellet will have two portions.In the result pictured, the microbunches in one portion arrivesimultaneously while the microbunches of the portion subjected to adifferent slope of differential acceleration arrive with some constantdistance between centers.

In general, multiple isotopic slugs provide means to shape the powerprofile on target. Peak power may be the most sought after factor, butefficient implosion may also require matching the input power to theaccelerating hydrodynamics and providing an appropriately timedpre-pulse of relatively low power to establish the fuel on a lowthermodynamic adiabat. This provides an especially large payoff when theplan uses fast ignition, where different processes are used to compressthe fuel and heat only enough fuel to ignition temperature to achievepropagating burn. In general, compression requires more input energythan the energy required to heat the fast ignition fuel mass by meansother than the compression itself. Creating the conditions in theabsorber that result in the high pressure needed to drive thecompression consumes part of the input energy, but much of the inputenergy also goes into the work of compressing the fuel. The lowestenergy to accomplish compression may be when the compressed state is atthe lowest temperature. Since the final temperature for any practicalcompression process will be related to the initial temperature, theleast energy to do the compression work will result with the initialtemperature being as low as practical.

In some embodiments, the slick input locations are based on the desiredspeed difference between slugs, the length of slugs going into theslick, and the gap between slugs needed to rephase the slick. The slicksfor longer slugs may be placed farther upstream from the pellet than theones for shorter slugs. A modest number of different slicks, e. g. 3 or4, may not be a cost problem in some embodiments where the energy kicksare ˜10ths of one % of the nominal beam energies, e.g., 50-200 MeV.

In some embodiments, different slicks may be electromagnetically “dead”during transit by the slugs they do not operate on. This timingoperation may readily fit into the timing necessitated by otherconsiderations discussed herein.

Some embodiments contemplate rephasing a slick's electromagnetic wavebetween slugs to shift from acceleration at the trailing end of thepreceding slug back to deceleration of the leading end of the followingslug. The rephasing requirement may reduce the intervening space betweenthe multiple slugs telescope. In some embodiments, the relationshipbetween the set of isotopes and their lengths before reaching the slickmay define the amount of energy that each provides to the pellet.

FIG. 11 depicts microbunch spacing within a slug in relation to a slickas contemplated in some embodiments. In some embodiments, operations atthe slick comprise the final adjustments before impact. These operationsmay begin at the last process that uses the phase space properties ofindividual microbunches, which have been preserved throughout previousbeam operations.

FIG. 12 depicts relative microbunch placement within a slug at varioustimes as occur in some embodiments. Practical beamline lengths mayrequire adequate differences between the nominal speeds of the multipleisotopes. While the speed differences for telescoping may be compensatedfor by the isotopes' correspondingly different masses, the speeddifferences may impact the processes that use RF accelerator structures.Linear accelerators may comprise physical structures supporting multipleaccelerating gaps with specific distances between them. Since efficientgeneration of high strength electromagnetic fields for accelerationrequires operating near a specific resonant frequency, time required fora particle to move from gap to gap can be similarly restricted, whichplaces a relatively tight requirement on the speeds of the particles.Independently phased cavities provide much greater ability to handle awide range of ion speeds. With appropriate consideration of cavity risetime, etc., computer control of the phase and amplitude wouldaccommodate SPRFD's needs. While independent phased cavities areunnecessary for the energy-input accelerator including the telescopesection, the flexibility of independently phased cavities may outweightheir increased cost for some of the beam manipulations.

In some embodiments, wobbler operation can result in (effectively)hollow beams at the pellet during the early and mid-stages of theimplosion. Creating a “hollow” beam may involve introducingperturbations to the beam dynamics that result in the beam spot movingaround a ring on the face of the target. Some wobbler designs excite RFstructures having much similarity to linear accelerators but aredesigned to impart periodic transverse accelerations to achieve thedesired perturbation of the beam dynamics rather than axialaccelerations to add energy to the ions. Other approaches provide thebeam-perturbations by different arrangements of electromagneticapparatus.

In some embodiments, pulsed magnetic beamline focusing elements locatedimmediately after the slick input may be programmed to input progressiveadjustments to the composite focal length, which may correlate with theregular progression of momentums from microbunch to microbunch in aslug. In some embodiments, the time for the isotopes to telescope fromthe slick positions translates to the maximum differential slick kickvelocity being within bounds for achromatic correction to mitigatechromatic aberration at the target. However, the discreteness andregularity of the microbunch to microbunch momentum differences lendthemselves to the dynamic compensation concept, and more fullycompensating the bunch-to-bunch momentum differences reduces themomentum spread toward that of each microbunch, about 0.1% from scaledHIDIF parameters. This value is substantially lower than many previousdesigns and is an important result of some embodiment's preservation ofthe microbunch structure.

Microbunch—Pre-Pellet Impact

In some embodiments, the profile for each isotope is tailored to improvethe effective and efficient use of the energy carried by a slug. FIG. 13illustrates the ability of the slick process to shape the temporalprofile of a slug in a variety of ways as may provide importantefficiencies in the pellet compression and ignition processes as mayoccur in some embodiments. The figure shows the slick RF waveformmodulated in time to have three different slopes for ease ofvisualization, although perfect linear waveforms are not required ingeneral and modulations that accommodate practical rise-times, etc. mayproduce superior results in some cases. As shown, the illustratedmodulation achieves a distinct early beam portion (pre-pulse) followedby a portion starting at low power (“foot”) and rising to high peakpower. Thus, by adding a feature to the modulation, this isotope cancontribute power to the foot, and remain on to contribute to the peakpower for compression and ignition, as illustrated in FIG. 10, and alsoprovide a pre-pulse and avoid the need to use one of the limited numberof isotopes for the pre-pulse alone.

FIG. 14 is a table depicting various relations between drivercomponents, energy, and other features as may occur in some embodiments.The bands of ranges in the pellet material for the different groups ofisotopes may be chosen for the design purpose of driving specificfeatures of the implosion and ignition of a fusion fuel pellet. Thetable illustrates the isotope features for use in HIF drivers. In someembodiments, the isotopes within each group have ranges in the materialsof fusion fuel targets that are close enough to drive a number ofdifferent features of the compression and ignition devised to improveefficiency and achieve the desired output of fusion energy. Theseadvantages are among several that are made possible in part by usingbeams of multiple telescoping isotopes.

Bragg Peak Generation and Operation Culmination

The microbunch duration at the pellet in FIG. 14 is based on maintainingthe microbunches at 800 MHz up to and through the differentialaccelerator. The microbunch momentum spread for this SPRFD configurationcan be 5E-4. This may also reduce the space charge force by the squareof the bunch length a factor of 6.25, which minimizes or eliminatespotential need for beam neutralization until the final phases ofgenerating a driver pulse. Lower momentum spread can translate toallowing longer drift distance for a given microbunch duration at thepellet.

Handling longer microbunches by maintaining them with lower frequency RFcavities may also reduce the space charge force by approximately thesquare of the bunch length. Therefore, using e.g. 800 MHz compared tofor example 2 GHz for microbunch maintenance may reduce the longitudinalspace charge force by a factor of 6.25. Such lower space charge forcescan reduce and may eliminate the potential need for beam neutralizationup to the entrance of the beams into the fusion chamber, where thecombination of telescoping and slicking cause the beam currents to riserapidly and the conditions for space charge and current neutralizationcan be provided.

Some embodiments contemplate using specified isotopes to employ theincreased energy deposition at their Bragg peaks to drive circularindentations or “waists” at specified axial stations in cylindricalpellets. As indicated in FIG. 14 and FIG. 1, these waists may sequesterthe relatively small masses of fusion fuel near the pellet's ends thatare slated for fast ignition (in either a cylindrical or sphericalconfiguration). In some embodiments, the waists will provide an “anvil”for the inward-moving hemispherical compression of the ends resultingfrom driving suitably shaped end caps. A further advantage of the waistsmay be to accomplish quasi-hemispherical compression of the inboard halfof the fast ignition zone, which may complement the hemisphericalcompression of the end caps and result in quasi-spherical compression ofthe fuel slated for fast ignition.

The increased efficiency of fast ignition can result from igniting afraction of the pre-compressed fuel. When fusion reactions begin in thishigh density (e.g., 100 g/cc) fuel, the fusion burn propagates rapidlyinto the rest of the high density fuel surrounding the fast ignitedportion. The temperature of the burning fuel may increase rapidly bymany-fold over the temperature required to ignite the burn (e.g., fromabout 10 keV to about 80 keV), which increases the vigor of the burn bythe attendant increase of about ten-fold in the reaction rate.

By designing the implosion to leave a channel containing relativelyhigh-density fuel at the centerline of the waists, the vigorouslyburning fuel in the end zones may propagate through the channel into thepreponderance of the fuel in the central region. This process may resultin the fusion burn propagating in the preponderance of fuel at lowerdensity than required for fast ignition. By reducing the requirement forthe energy-consuming compression of the larger portion of the fuel, thisprocess may realize a substantial increase in the overall ratio offusion fuel output input beam energy, e.g., lower the required beamenergy for a given fusion yield. For example, while fast ignition mayrequire fuel density like 100 g/cc to achieve with a 50 μm radius spot,the central fuel region may achieve ρR˜0.5 g/cm² with a density of 10g/cc and a zone heated to ignition temperature that is 0.5 mm in radius,with fusion yield of about 10 GJ from 30% burn-up of the fuel in acentral region one centimeter long, and a convergence ratio of aboutseven for cylindrical compression from the 0.2 g/cc density of frozen DTto 10 g/cc.

FIG. 14 indicates reasonable placement of the Bragg peaks of groups andisotopes within groups. Different isotopes may be used to adjust theshown placements. The ranges may aid high energy density facilitiesunder development to provide elevated target temperatures.

In some embodiments, microbunch stretching during the flight from theslick input to the pellet may set the maximum allowable length at theslick input to meet the requirements that the microbunch length be ≤theslug length at the pellet and that the slug duration mesh with itsspecified role in building the overall pulse profile. SPRFD may uselarger pellets with larger fusion yields for reasons involving realismof the implosion processes and economics. Generally, long, relativelyslow implosions may affect the accelerator physics favorably.

Greater energy input can imply a lower compression requirement for thebulk of the fuel, with peak fuel density like the 100 g/cc.

In some embodiments, the Bragg peak of the fastest, longest-rangeisotope may penetrate beyond the far end of the cylinder, but the Braggpeaks of some isotopes may be arranged to occur at two significantlongitudinal positions. FIG. 14 shows isotopes selected with theirrelative kinetic energies set by the telescoping condition to experiencetheir Bragg peaks at axial locations approximately the diameter of theinitial fuel zone in the end regions, to facilitate quasi-sphericalcompression of the fuel slated for fast ignition in those end zones. Theresulting increased intensity of the energy deposition may create asphincter in the cylindrical implosion that provides a complementarybackward motion for the implosion of the end caps by the shortest-rangeslugs. In some embodiments, the quasi-hemispherical implosion of the endcaps becomes a quasi-spherical implosion of fuel in end “cells”.

The convergence factor may drive the requirements for symmetry, evennessof heating, instability growth, manufacturing tolerances, etc. To attaina given density, the convergence factor may be less for spherical thancylindrical implosions. To the extent the end cells takes the shape ofquasi-spheres compressed to fast ignition density, the convergencerequirement may reduce from the factor for plain cylindrical toward thelesser factor of spherical, e.g. the “sausage link” of fuel between themmay allow lower density.

To a degree, burn propagation into less dense fuel beyond the reducedregion in a volume of lower density fuel may be similar to that aspectof the X-pellet fusion heat from the fast-ignited end cells propagatingthrough the necked down zone being adequate to heat fuel that meets theR requirement ˜1 g/cm2. In some embodiments, less energy is needed tocompress the “sausage link” if lower fuel density will suffice.

Telescoping

FIG. 15 depicts a plurality of microbunches prior to impact in someembodiments. Various features of this process are described in greaterdetail in U.S. Pub. No. 2012-0328066 “Single-pass, heavy ion fusion,systems and method for fusion power production and other applications ofa large-scale neutron source”, incorporated by reference herein in itsentirety.

Wobblering may occur at a diversity of ion speeds. At the compressionpeak, beam wobble may nearly be zero, and may be zero for fast ignitionon the beam's axis. Wobblering may include a conically tapered helix.The tapered helix can be made up of microbunches and may not be acontinuous thread, although the microbunches can be thoroughlyoverlapped at the pellet. As a consequence of the helical shape thestructure may be referred to as “hollow.” The location of the beamcentroid may be modulated by a section of RF accelerator say 50-100 mfrom the pellet. Wobblering may also focus the beam. The beam that iswobbled can converge similar to a cone—the essence of strong focusing isthat the beams squish in one direction while expanding in the other, andthe shape at the target can be circular or elliptical.

With narrow bandwidth wobbler designs, using a small number (2 or 3)wobblers in series is reasonable, to an extent. Independently phased RFwobbler cavities may be used in some embodiments and the cost to applygiven RF field strengths by a multiplicity of cavities and relativelysmall RF sources may be offset by the economies of production methodsfor high quantities, such as automation.

Were a narrow bandwidth wobbler to be used, the widening of the annularthickness of beams of ions with speeds that differ appreciably from thatfor which the wobbler is designed may be beneficial for driving the endcaps in some embodiments. For example, a wobbler's effect to spread thenominal 50 μm spot for off-speed ions may improve the heating symmetryand benefit implosion dynamics. Symmetry and smoothness of heating maybe critical for achieving well-behaved hydrodynamics and goodthermodynamic results. Because the end caps are ˜1 cm radius, drivingthem with a beam concentrated to a small spot like 50 μm, i.e. awobblered ring 50 μm in half-width, may result in a bump in pressurethat would ruin the compression process. If the spot is not effectivelyenlarged by a wobbler in this manner, other means may be used to enlargethe beam spot as necessary.

Some embodiments reflect that symmetry and smoothness of heating iscritical for achieving good hydrodynamics and good thermodynamicresults. The end caps may be ˜1 cm radius in some embodiments. Inembodiments concentrating the beam on 50 μm, e.g. a wobblered ring 50 μmin half-width, the resulting bump in pressure may mess up thecompression process.

Energy Deposition

FIG. 16 is a plot of the axial profile of the beam energy depositionrate showing the substantial increase in the rate of energy depositionexhibited by heavy ions near the end of the range. The “Bragg peaks” maygenerally occur in the region with this higher rate of energydeposition. The resultant increased specific heating of the absorbermaterial may be used to increase the pressure generated in the stoppingmaterial in the vicinity of the Bragg peak relative to the adjacentmaterial. For cylindrical pellets, this higher pressure may be used toaccelerate the implosion at those locations and cause a sphincter-likemotion to cinch waists into the pellet.

Beam Formation

FIG. 17 depicts merging of beams in parallel linear accelerators. Someembodiments select an isotope mass which gives the energies for a set ofisotopes through the telescoping condition, βγA¼ constant for commonmagnetic rigidity (chargestate +1 forall). Some “fine tuning” of therange may be provided by practical nuclide options with different A/Z.

In some embodiments, the merge step trades an increase in transverseemittance of the 4-fold decreasing longitudinal emittance accomplishedby Loop-Back Delay Lines. The transverse emittance increase may be heldto a minimum by combining the beams in two steps, one using each of thetransverse planes. In some embodiments, this is the only beammanipulation in the entire ignition pulse generator that intentionallyincreases the transverse emittance. Therefore, in some embodiments themerge defines the smallest possible transverse emittance at the targetto be the emittance output from the linear accelerator times theincrease of the merge.

FIG. 18 illustrates the relative locations of the elements along thesection of beamline that terminates at the fusion fuel pellet in someembodiments. The figure shows the final beam compression elements ofSlick (different Slickers for two different Groups of Isotopes) andlens, and the Wobbler that creates the effect of a hollow beam at thepellet as may be used to drive cylindrical targets in some embodiments.

Dynamic Compensation for Microbunch to Microbunch Momentum Differences

FIG. 19 depicts a dynamic, compound beamline element to adjust theoverall focal length of the transport and focusing system from theSlicker to the fusion fuel pellet on a microbunch-to-microbunch basis asimplemented in some embodiments. This dynamic beamline element providescorrection for the focal-plane shifts that otherwise would occur becauseof the differences in momentum from microbunch to microbunch that wereinput to cause the Slick process. Such correction can be possiblebecause the amplitude of these discrete momentum differences are in aregular progression that can be addressed by a dynamic focusing elementwith correspondingly regular effects on the series of microbunches in aslug.

In some embodiments, compensation mitigates the tendency for focalpoints of different microbunches to shift because of the differentialacceleration (which may be up to 72-3% for some isotopes). Because thedifferences in momentum between microbunches may be correlated andregular, time-ramped beamline transport elements 1905 immediatelyfollowing the differential accelerator in some embodiments can partiallycorrect the associated shifts of focal point (FIG. 19) after the slickthat operates on a microbunch-by-microbunch basis to compensate for thenormal effect of the microbunch-by-microbunch momentum differences toshift the position of the ultimate focal point.

This time varying element in the transfer matrix may be located shortlyafter output from the differential accelerator, were the microbunchesremain axially separate. The duration of the dynamic magnetic waveformmay range from r100 ns to 600 ns, for the various isotopes. Thecorrelated amplitude change between consecutive microbunches can be 2/Nof the maxima at the isotope's ends, where N is the number ofmicrobunches in the isotope.

This process may trend the net chromatic effects at the pellet towardthe lower limit of the longitudinal phase space of a single microbunch.This minimum momentum spread, scaled from HIDIF parameters, may beestimated to be about 0.04% for the 800 MHz embodiment of SPRFD,compared to 0.1% for the 2 GHz embodiment.

In some embodiments, a dynamic beam line element may be located justdownstream of the differential accelerator. The beam line element maycorrect for the discrete axial shifts of the ultimate focal point on thepellet due to the discrete changes in the nominal moment successivemicrobunches. Where the microbunches remain separated axially. Chromaticand geometrical correction may be applied in some embodiments. Beamtransport across the chamber, with modest vacuum r10^(┘) 4 Torr, mayfavor neutralized transport, preferably with pre-ionization.

Providing electrons to make the beam neutral, e.g., as in “normal”plasma, can prevent the “space charge” of the beam from pushing itapart. This method pre-ionizes the beam channels so that the mobileelectrons move so as to neutralize the space charge.

In some embodiments, the slow 1 pp of FPC's chambers eliminateselectromagnetic disturbances from previous pulses. In some embodiments,the environment may be damped out on a 10 ms time scale as a result ofthe thorough disruption and recovery of patterns of stream jets, sheets,droplet sprays, tangential flows along the chamber walls, and regulatedfountains from below the fusion reaction zone. In some embodiments, afinal 30 cm cone hollowed in the room-temperature lithium sabot may haveinternal target reticle-films, and also may have a captured atmospherewith a specific gas and optimal density, if helpful to focusing. Allthese features may derive from slow pulsing fusion yields (e.g., 10 GWthper chamber), achieved by an accordingly large driver. The lens borevolumes may likewise benefit from slow pulsing. In some embodiments,lithium's adsorption pump benefit is naturally adapted to maintainingquite low neutral density in the bore tubes.

Finally, whereas all other chambers may inject lithium at temperaturesnot far below the desired working fluid hotside temperature, presentembodiments contemplate that a chamber injects lithium at temperaturesin the vicinity of its melting point, where the lithium vapor pressureis even lower than in other designs, providing even higher pumping speedand recovery of desirable chamber conditions.

General Benefits of Certain Embodiments

The discussed approach in some embodiments has several benefits,including e.g. 1) reduce the convergence factor where the highestcompression is needed by approaching spherical compression geometry, and(2) relieve compression requirements on the bulk of the fuel bypropagating the burn that was fast ignited through the neck and intofuel at lower density.

Remarks

In general, the routines executed to implement the embodiments of thedisclosure, may be implemented as part of an operating system or aspecific application, component, program, object, module or sequence ofinstructions referred to as “computer programs.” The computer programstypically comprise one or more instructions set at various times invarious memory and storage devices in a computer, and that, when readand executed by one or more processing units or processors in acomputer, cause the computer to perform operations to execute elementsinvolving the various aspects of the disclosure.

Moreover, while embodiments have been described in the context of fullyfunctioning computers, computer systems, control circuits for RFcavities, etc., those skilled in the art will appreciate that thevarious embodiments are capable of being distributed as a programproduct in a variety of forms, and that the disclosure applies equallyregardless of the particular type of machine or computer-readable mediaused to actually effect the distribution.

Unless the context clearly requires otherwise, throughout thedescription and the claims, the words “comprise,” “comprising,” and thelike are to be construed in an inclusive sense, as opposed to anexclusive or exhaustive sense; that is to say, in the sense of“including, but not limited to.” As used herein, the terms “connected,”“coupled,” or any variant thereof, means any connection or coupling,either direct or indirect, between two or more elements; the coupling ofconnection between the elements can be physical, logical, or acombination thereof. Additionally, the words “herein,” “above,” “below,”and words of similar import, when used in this application, shall referto this application as a whole and not to any particular portions ofthis application. Where the context permits, words in the above DetailedDescription using the singular or plural number may also include theplural or singular number respectively. The word “or,” in reference to alist of two or more items, covers all of the following interpretationsof the word: any of the items in the list, all of the items in the list,and any combination of the items in the list.

The above detailed description of embodiments of the disclosure is notintended to be exhaustive or to limit the teachings to the precise formdisclosed above. While specific embodiments of, and examples for, thedisclosure are described above for illustrative purposes, variousequivalent modifications are possible within the scope of thedisclosure, as those skilled in the relevant art will recognize. Forexample, while processes or blocks are presented in a given order,alternative embodiments may perform routines having steps, or employsystems having blocks, in a different order, and some processes orblocks may be deleted, moved, added, subdivided, combined, and/ormodified to provide alternative or subcombinations. Each of theseprocesses or blocks may be implemented in a variety of different ways.Also, while processes or blocks are at times shown as being performed inseries, these processes or blocks may instead be performed in parallel,or may be performed at different times. Further, any specific numbersnoted herein are only examples: alternative implementations may employdiffering values or ranges.

The teachings of the disclosure provided herein can be applied to othersystems, not necessarily the system described above. The elements andacts of the various embodiments described above can be combined toprovide further embodiments.

These and other changes can be made to the disclosure in light of theabove Detailed Description. While the above description describescertain embodiments of the disclosure, and describes the best modecontemplated, no matter how detailed the above appears in text, theteachings can be practiced in many ways. Details of the system may varyconsiderably in its implementation details, while still beingencompassed by the subject matter disclosed herein. As noted above,particular terminology used when describing certain features or aspectsof the disclosure should not be taken to imply that the terminology isbeing redefined herein to be restricted to any specific characteristics,features, or aspects of the disclosure with which that terminology isassociated. In general, the terms used in the following claims shouldnot be construed to limit the disclosure to the specific embodimentsdisclosed in the specification, unless the above Detailed Descriptionsection explicitly defines such terms. Accordingly, the actual scope ofthe disclosure encompasses not only the disclosed embodiments, but alsoall equivalent ways of practicing or implementing the disclosure underthe claims.

While certain aspects of the disclosure are presented below in certainclaim forms, the inventors contemplate the various aspects of thedisclosure in any number of claim forms. For example, while only oneaspect of the disclosure is recited as a means-plus-function claim under35 U.S.C. § 112, ¶6, other aspects may likewise be embodied as ameans-plus-function claim, or in other forms, such as being embodied ina computer-readable medium. (Any claims intended to be treated under 35U.S.C. § 112, ¶6 will begin with the words “means for”.) Accordingly,the applicant reserves the right to add additional claims after filingthe application to pursue such additional claim forms for other aspectsof the disclosure.

What is claimed is:
 1. A method for compressing a fuel source, themethod comprising: receiving a first plurality of ions, each ioncomprising one of a plurality of isotopes; segregating the firstplurality of ions based upon their corresponding isotopes into a firstplurality of microbunches; separating the first plurality ofmicrobunches in space by applying a first electromagnetic wave; reducingthe distance between the microbunches of the first plurality ofmicrobunches; differentially accelerating the first plurality ofmicrobunches; reducing the distance between a center of mass of thefirst plurality of ions and a center of mass of a second plurality ofions; and colliding the first plurality of ions and the second pluralityof ions with one or more layers such that compression of the one or morelayers is maximized by the positionally higher pressure resulting fromone or more Bragg peaks associated with the first plurality of ions andthe second plurality of ions.
 2. The method of claim 1, wherein the oneor more layers cover at least a portion of a cylindrical fuel source. 3.The method of claim 1, wherein the one or more layers cover at least aportion of a spherical fuel source.
 4. The method of claim 1, whereinthe frequency of the first electromagnetic wave is approximately 800MHz.
 5. The method of claim 1, further comprising: segregating thesecond plurality of ions based upon their corresponding isotopes into asecond plurality of microbunches; separating the second plurality ofmicrobunches in space by applying a second electromagnetic wave; andincreasing the frequency of the second electromagnetic wave to reducethe distance between the microbunches of the second plurality ofmicrobunches.
 6. The method of claim 1, wherein the first plurality ofions is configured to drive the fuel source at a waist region.
 7. Themethod of claim 1, wherein the second plurality of ions is configured tocompress end caps located in the fuel chamber.